Don Peebles, the son of a mechanic, built a real-estate empire that includes three palatial family homes in the Hamptons, Washington, D.C., and Coral Gables, Fla.

As the founder and chairman of a multi-billion-dollar real-estate development and investment company, Don Peebles knows how to hold out for a deal.

"I was sitting in Miami one summer, and it was so hot," Mr. Peebles recalled. So in 2004, he started to look for someplace cooler—and found an 11-acre compound in Bridgehampton, N.Y., listed for around $20 million, he said. He waited as it came down to $9 million, then $5.95...